Is the correct affiliation with the Ahl as-Sunnah wal-Jama'ah, or with the Pious Predecessors (Salaf as-Salih)?

Both statements are correct. The Pious Predecessors (Salaf as-Salih) are the essence of Ahl as-Sunnah (definition) wal-Jama'ah, and following them is a criterion for identifying Ahl as-Sunnah. True affiliation is demonstrated through speech, belief, and action. Sheikh Ibn Baz was asked about denying affiliation with Ahl as-Sunnah wal-Jama'ah and preferring affiliation with the Salaf. He replied that the Salaf are Ahl as-Sunnah wal-Jama'ah, and affiliating with them is a right, as it is an affiliation with the people of truth, not falsehood. The one who affiliates must strive to be truthful in their claim.